Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/77

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The Analyst.
67

which are produced in Moments or infinitely ſmall Parts of Time, are alone proportional to given Velocities: That, therefore, in order to conceive the firſt Fluxions, we muſt conceive Time divided into Moments, Increments generated in thoſe Moments, and Velocities proportional to thoſe Increments: That in order to conceive ſecond and third Fluxions, we muſt ſuppoſe that the naſcent Principles or momentaneous Increments have themſelves alſo other momentaneous Increments, which are proportional to their reſpective generating Velocities: That the Velocities of theſe ſecond momentaneous Increments are ſecond Fluxions: thoſe of their naſcent momentaneous Increments third Fluxions. And ſo on ad infinitum.


XLIII. By ſubducting the Increment generated in the firſt Moment from that generated in the ſecond, we get the Increment of an Increment. And by ſubducting the Velocity generating in the firſt Moment from that generating in the ſecond, we get the Fluxion of a Fluxion. In like manner, by ſubducting the Difference of

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